The evolution of Internet of Things (IoT) networks has been studied owing to the associated benefits in useful applications. Although the evolution is highly helpful, the increasing day-to-day demands of mobile users have led to immense requirements for further performance improvements such as efficient spectrum utilization, massive device connectivity, and high data rates. Fortunately, reconfigurable intelligent surfaces (RIS) and non-orthogonal multiple access (NOMA) techniques have recently been introduced as two possible current-generation emerging technologies with immense potential of addressing the above-mentioned issues. In this paper, we propose the integration of RIS to the existing techniques (i.e., NOMA and relaying) to further enhance the performance for mobile users. We focus on a performance analysis of two-user group by exploiting two main performance metrics including outage probability and ergodic capacity. We provide closed-form expressions for both performance metrics to highlight how NOMA-aided RIS systems provide more benefits compared with the benchmark based on traditional orthogonal multiple access (OMA). Monte-Carlo simulations are performed to validate the correctness of obtained expressions. The simulations show that power allocation factors assigned to two users play a major role in the formation of a performance gap among two users rather than the setting of RIS. In particular, the strong user achieves optimal outage behavior when it is allocated 35% transmit power.